{"paper":{"title":"Non existence of constant mean curvature graphs on circular annuli of $\\mathbb{H}^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Cosimo Senni","submitted_at":"2010-11-30T15:40:24Z","abstract_excerpt":"We show a non existence result for solutions of the prescribed mean curvature equation in the product manifold $\\mathbb{H}^2 \\times \\R$, where $\\mathbb{H}^2$ is the real hyperbolic plane. More precisely we prove a-priori estimates for graphs with constant mean curvature $h \\in (0, 1/2]$ on circular annuli of $\\mathbb{H}^2$. For $0 < h < 1/2$ we obtain an estimate from above on any circular annulus and one from below on annuli with a small hole, the size of the hole depending on $h$. For $h = 1/2$ we obtain both estimates for any circular annulus. All the estimates depend only on the thickness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6583","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}